Application of fixed point transformation to classical model identification using new tuning rule

Abstract

Up to now the fundamental tool of adaptive nonlinear control design is Lyapunov's 2nd or "Direct" Method. Recently the Sigmoid Generated Fixed Point Transformation (SGFPT) has been introduced for evading the application of the Lyapunov technique. This systematic method has been presented for the generation of whole families of Fixed Point Transformations and has been extended from Single Input Single Output (SISO) to Multiple Input Multiple Output (MIMO) systems. Few studies have been revealed that the original Robust Fixed Point Transformation (RFPT) can be successfully combined with some modification of the classical methods, such as the Modified Adaptive Inverse Dynamic Robot Controller (MAIDRC) and the Modified Adaptive Slotine-Li Robot Controller (MADSLRC). This paper presents that the SGFPT can also well coexist with the MAIDRC control design. Additionally, a novel, even more simplified tuning technique is proposed that also applies fixed point transformation-based tuning rule for parameter identification. The theoretical considerations are validated by numerical simulations made for a 2 Degree of Freedom (DoF) paradigm, in the adaptive control of two coupled mass-points with simultaneous parameter identification.